Low-rank regularized image-domain least-squares migration with a fast point-spread function calculation approach

Abstract By solving a linear inverse problem to correct the Hessian effects, least-squares migration (LSM) has become a routine for high-resolution and amplitude-preserving imaging. Unlike data-domain LSM, the image-domain LSM that is based on the point spread functions (PSFs) does not require the computationally intensive Born modeling and adjoint migrations, which provides a more efficient and practical alternative for high-resolution imaging. The key challenge in PSF-based image-domain LSM is the efficient computation of PSFs and the stable implementation of reflectivity inversion. To mitigate these issues, we present a fast PSF calculation method using a Gaussian beam propagator. By applying a saddle-point approximation to the integrals over ray parameters, our approach computes PSFs using a single wavefield extrapolation for all sources and receivers. Moreover, local plane-wave decomposition at beam centers further reduces the number of Green's function calculations. These two optimization strategies allow for efficient PSF computation. In reflectivity inversion, a local low-rank regularization is introduced in image-domain LSM to improve inversion stability and suppress migration artifacts. The low-rank regularized least-squares problem is solved using the alternating direction method of multipliers (ADMM). PSF convolution and deconvolution, combined with an optimized Gaussian partition of unity, are used in the ADMM framework to avoid constructing the entire Hessian matrix. Numerical experiments for synthetic and field data verify the feasibility of the proposed method and demonstrate the adaptability for low signal-to-noise-ratio data.